Algebra II : Addition and Subtraction

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #81 : Addition And Subtraction

Add the following numbers:  \displaystyle 419+841+542

Possible Answers:

\displaystyle 1792

\displaystyle 1798

\displaystyle 1820

\displaystyle 1802

\displaystyle 1702

Correct answer:

\displaystyle 1802

Explanation:

Add the ones digits.

\displaystyle 9+1+2 =12

The carryover is the tens place.

Add the tens digits.

\displaystyle 1+4+4+(1) = 10

The carryover for the next calculation is the tens place.

\displaystyle 4+8+5+(1) = 18

Combine this number with the ones digits of the previous calculations.

The answer is:  \displaystyle 1802

Example Question #81 : Addition And Subtraction

Add the following numbers:  \displaystyle 1264+9811

Possible Answers:

\displaystyle 11075

\displaystyle 9975

\displaystyle 10075

\displaystyle 9895

\displaystyle 12075

Correct answer:

\displaystyle 11075

Explanation:

Add the ones digits.

\displaystyle 4+1=5

There is no carryover.

Add the tens digits.

\displaystyle 6+1=7

There is also no carryover.

Add the hundreds digits.

\displaystyle 2+8 = 10

The carryover is the tens digit.

Add the thousands digits with the carryover.

\displaystyle 1+9+(1) = 11

Combine this value with the ones digits of the previous calculations.

The answer is:  \displaystyle 11075

Example Question #82 : Addition And Subtraction

Add the numbers:  \displaystyle 879+654

Possible Answers:

\displaystyle 1553

\displaystyle 1423

\displaystyle 1533

\displaystyle 1443

\displaystyle 1323

Correct answer:

\displaystyle 1533

Explanation:

Add the ones digits.

\displaystyle 9+4 = 13

The carryover is the tens digit.

Add the tens digits with the carryover.

\displaystyle 7+5+(1) =13

The carryover is the tens digit.

\displaystyle 8+6+(1) =15

Combine this value with the one digits of the previous calculations.

The answer is:  \displaystyle 1533

Example Question #83 : Addition And Subtraction

Add the following numbers:  \displaystyle 318+219+797

Possible Answers:

\displaystyle 1224

\displaystyle 1234

\displaystyle 1334

\displaystyle \textup{The answer is not given.}

\displaystyle 1324

Correct answer:

\displaystyle 1334

Explanation:

Add the ones digits.

\displaystyle 8+9+7 = 24

Carry over the tens digit to the next calculation.

Add the tens digits with the carryover.

\displaystyle 1+1+9+(2) = 13

Repeat the process for the hundreds digits.

\displaystyle 3+2+7+(1) = 13

Combine this number with the ones digits of the previous calculations.

The answer is:  \displaystyle 1334

Example Question #84 : Addition And Subtraction

Add the following numbers:  \displaystyle 49+81+79+24+99

Possible Answers:

\displaystyle \textup{The answer is not given.}

\displaystyle 292

\displaystyle 332

\displaystyle 342

\displaystyle 322

Correct answer:

\displaystyle 332

Explanation:

Add the ones digits.

\displaystyle 9+1+9+4+9 = 32

Add the tens digit with the carryover, 3.

\displaystyle 4+8+7+2+9+(3) = 33

Combine this number with the ones digit of the first number.

The answer is:  \displaystyle 332

Example Question #81 : Addition And Subtraction

Subtract the following numbers:  \displaystyle 95-15-85-87-31

Possible Answers:

\displaystyle -123

\displaystyle \textup{The answer is not given.}

\displaystyle -96

\displaystyle -103

\displaystyle -37

Correct answer:

\displaystyle -123

Explanation:

We cannot subtract the numbers like how we can easily add numbers.  As a result, we will have to subtract each number at a time and this may be time consuming.

However, in order to save calculation time, we can simply take out a common factor of negative one so that we can add all the positive terms, and then subtract. 

\displaystyle 95-15-85-87-31 = -1(-95+[15+85+87+31])

\displaystyle = -1(-95+[218])

We can then rearrange the numbers to subtract.

\displaystyle -1(218-95)

Subtract the ones digits.

\displaystyle 8-5 = 3

Borrow a one from the 2 in 218 and then subtract the tens digits.  The hundreds digit becomes a 1.

\displaystyle 11-9 = 2

Combine the hundreds digit with the other ones digits.  The expression becomes:

\displaystyle -1(218-95) = -1(123) = -123

The answer is:  \displaystyle -123

Example Question #2291 : Mathematical Relationships And Basic Graphs

Add the following numbers:  \displaystyle 974+316+163

Possible Answers:

\displaystyle 1453

\displaystyle 1443

\displaystyle 1553

\displaystyle 1543

\displaystyle 1253

Correct answer:

\displaystyle 1453

Explanation:

Add the ones digits.

\displaystyle 4+6+3=13

Add the tens digits with the one as the carryover.

\displaystyle 7+1+6+(1)=15

Add the hundreds digits with the new carryover.

\displaystyle 9+3+1+(1) =14

Combine this number with the ones digits of the previous numbers.

The answer is:  \displaystyle 1453

Example Question #85 : Addition And Subtraction

Add the numbers:  \displaystyle 974+978+192

Possible Answers:

\displaystyle 2054

\displaystyle 2114

\displaystyle 2144

\displaystyle 2244

\displaystyle 2034

Correct answer:

\displaystyle 2144

Explanation:

Add the ones digits.

\displaystyle 4+8+2 = 14

Add the tens digits with the one as the carryover.

\displaystyle 7+7+9+(1)= 24

Add the hundreds digits with the two as the carryover.

\displaystyle 9+9+1+(2) = 21

Combine this number with the ones digits of the previous calculations.

The answer is:  \displaystyle 2144

Example Question #81 : Addition And Subtraction

Add the following:  \displaystyle 644+494+911

Possible Answers:

\displaystyle 2039

\displaystyle 2049

\displaystyle 1949

\displaystyle \textup{The answer is not given.}

\displaystyle 2029

Correct answer:

\displaystyle 2049

Explanation:

Add the ones digits.

\displaystyle 4+4+1= 9

Add the tens digits.  There is no carryover.

\displaystyle 4+9+1 = 14

Add the hundreds digits.   The carryover is 1.

\displaystyle 6+4+9+(1) = 20

Combine this number with the ones digits of the previous calculations.

The answer is:  \displaystyle 2049

Example Question #2292 : Mathematical Relationships And Basic Graphs

Add the following numbers:  \displaystyle 856+196+877

Possible Answers:

\displaystyle 1819

\displaystyle 1939

\displaystyle 1829

\displaystyle \textup{The answer is not given.}

\displaystyle 1929

Correct answer:

\displaystyle 1929

Explanation:

Add the ones digits.

\displaystyle 6+6+7 = 19

Add the tens digits with the 1 as the carryover.

Add the tens digits.

\displaystyle 5+9+7+(1) = 22

Add the hundreds digits with the 2 as the carryover.

\displaystyle 8+1+8+(2) = 19

Combine this value with the ones digits of the first two calculations.

The answer is:  \displaystyle 1929

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